Polytope of Type {86,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {86,10}*1720
Also Known As : {86,10|2}. if this polytope has another name.
Group : SmallGroup(1720,35)
Rank : 3
Schlafli Type : {86,10}
Number of vertices, edges, etc : 86, 430, 10
Order of s0s1s2 : 430
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {86,2}*344
10-fold quotients : {43,2}*172
43-fold quotients : {2,10}*40
86-fold quotients : {2,5}*20
215-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 43)( 3, 42)( 4, 41)( 5, 40)( 6, 39)( 7, 38)( 8, 37)( 9, 36)
( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 30)( 16, 29)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 45, 86)( 46, 85)( 47, 84)
( 48, 83)( 49, 82)( 50, 81)( 51, 80)( 52, 79)( 53, 78)( 54, 77)( 55, 76)
( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 63, 68)
( 64, 67)( 65, 66)( 88,129)( 89,128)( 90,127)( 91,126)( 92,125)( 93,124)
( 94,123)( 95,122)( 96,121)( 97,120)( 98,119)( 99,118)(100,117)(101,116)
(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109)(131,172)
(132,171)(133,170)(134,169)(135,168)(136,167)(137,166)(138,165)(139,164)
(140,163)(141,162)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156)
(148,155)(149,154)(150,153)(151,152)(174,215)(175,214)(176,213)(177,212)
(178,211)(179,210)(180,209)(181,208)(182,207)(183,206)(184,205)(185,204)
(186,203)(187,202)(188,201)(189,200)(190,199)(191,198)(192,197)(193,196)
(194,195)(217,258)(218,257)(219,256)(220,255)(221,254)(222,253)(223,252)
(224,251)(225,250)(226,249)(227,248)(228,247)(229,246)(230,245)(231,244)
(232,243)(233,242)(234,241)(235,240)(236,239)(237,238)(260,301)(261,300)
(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)(269,292)
(270,291)(271,290)(272,289)(273,288)(274,287)(275,286)(276,285)(277,284)
(278,283)(279,282)(280,281)(303,344)(304,343)(305,342)(306,341)(307,340)
(308,339)(309,338)(310,337)(311,336)(312,335)(313,334)(314,333)(315,332)
(316,331)(317,330)(318,329)(319,328)(320,327)(321,326)(322,325)(323,324)
(346,387)(347,386)(348,385)(349,384)(350,383)(351,382)(352,381)(353,380)
(354,379)(355,378)(356,377)(357,376)(358,375)(359,374)(360,373)(361,372)
(362,371)(363,370)(364,369)(365,368)(366,367)(389,430)(390,429)(391,428)
(392,427)(393,426)(394,425)(395,424)(396,423)(397,422)(398,421)(399,420)
(400,419)(401,418)(402,417)(403,416)(404,415)(405,414)(406,413)(407,412)
(408,411)(409,410);;
s1 := ( 1, 2)( 3, 43)( 4, 42)( 5, 41)( 6, 40)( 7, 39)( 8, 38)( 9, 37)
( 10, 36)( 11, 35)( 12, 34)( 13, 33)( 14, 32)( 15, 31)( 16, 30)( 17, 29)
( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 44,174)( 45,173)( 46,215)
( 47,214)( 48,213)( 49,212)( 50,211)( 51,210)( 52,209)( 53,208)( 54,207)
( 55,206)( 56,205)( 57,204)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)
( 63,198)( 64,197)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)
( 71,190)( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,183)
( 79,182)( 80,181)( 81,180)( 82,179)( 83,178)( 84,177)( 85,176)( 86,175)
( 87,131)( 88,130)( 89,172)( 90,171)( 91,170)( 92,169)( 93,168)( 94,167)
( 95,166)( 96,165)( 97,164)( 98,163)( 99,162)(100,161)(101,160)(102,159)
(103,158)(104,157)(105,156)(106,155)(107,154)(108,153)(109,152)(110,151)
(111,150)(112,149)(113,148)(114,147)(115,146)(116,145)(117,144)(118,143)
(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)
(127,134)(128,133)(129,132)(216,217)(218,258)(219,257)(220,256)(221,255)
(222,254)(223,253)(224,252)(225,251)(226,250)(227,249)(228,248)(229,247)
(230,246)(231,245)(232,244)(233,243)(234,242)(235,241)(236,240)(237,239)
(259,389)(260,388)(261,430)(262,429)(263,428)(264,427)(265,426)(266,425)
(267,424)(268,423)(269,422)(270,421)(271,420)(272,419)(273,418)(274,417)
(275,416)(276,415)(277,414)(278,413)(279,412)(280,411)(281,410)(282,409)
(283,408)(284,407)(285,406)(286,405)(287,404)(288,403)(289,402)(290,401)
(291,400)(292,399)(293,398)(294,397)(295,396)(296,395)(297,394)(298,393)
(299,392)(300,391)(301,390)(302,346)(303,345)(304,387)(305,386)(306,385)
(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)(313,378)(314,377)
(315,376)(316,375)(317,374)(318,373)(319,372)(320,371)(321,370)(322,369)
(323,368)(324,367)(325,366)(326,365)(327,364)(328,363)(329,362)(330,361)
(331,360)(332,359)(333,358)(334,357)(335,356)(336,355)(337,354)(338,353)
(339,352)(340,351)(341,350)(342,349)(343,348)(344,347);;
s2 := ( 1,259)( 2,260)( 3,261)( 4,262)( 5,263)( 6,264)( 7,265)( 8,266)
( 9,267)( 10,268)( 11,269)( 12,270)( 13,271)( 14,272)( 15,273)( 16,274)
( 17,275)( 18,276)( 19,277)( 20,278)( 21,279)( 22,280)( 23,281)( 24,282)
( 25,283)( 26,284)( 27,285)( 28,286)( 29,287)( 30,288)( 31,289)( 32,290)
( 33,291)( 34,292)( 35,293)( 36,294)( 37,295)( 38,296)( 39,297)( 40,298)
( 41,299)( 42,300)( 43,301)( 44,216)( 45,217)( 46,218)( 47,219)( 48,220)
( 49,221)( 50,222)( 51,223)( 52,224)( 53,225)( 54,226)( 55,227)( 56,228)
( 57,229)( 58,230)( 59,231)( 60,232)( 61,233)( 62,234)( 63,235)( 64,236)
( 65,237)( 66,238)( 67,239)( 68,240)( 69,241)( 70,242)( 71,243)( 72,244)
( 73,245)( 74,246)( 75,247)( 76,248)( 77,249)( 78,250)( 79,251)( 80,252)
( 81,253)( 82,254)( 83,255)( 84,256)( 85,257)( 86,258)( 87,388)( 88,389)
( 89,390)( 90,391)( 91,392)( 92,393)( 93,394)( 94,395)( 95,396)( 96,397)
( 97,398)( 98,399)( 99,400)(100,401)(101,402)(102,403)(103,404)(104,405)
(105,406)(106,407)(107,408)(108,409)(109,410)(110,411)(111,412)(112,413)
(113,414)(114,415)(115,416)(116,417)(117,418)(118,419)(119,420)(120,421)
(121,422)(122,423)(123,424)(124,425)(125,426)(126,427)(127,428)(128,429)
(129,430)(130,345)(131,346)(132,347)(133,348)(134,349)(135,350)(136,351)
(137,352)(138,353)(139,354)(140,355)(141,356)(142,357)(143,358)(144,359)
(145,360)(146,361)(147,362)(148,363)(149,364)(150,365)(151,366)(152,367)
(153,368)(154,369)(155,370)(156,371)(157,372)(158,373)(159,374)(160,375)
(161,376)(162,377)(163,378)(164,379)(165,380)(166,381)(167,382)(168,383)
(169,384)(170,385)(171,386)(172,387)(173,302)(174,303)(175,304)(176,305)
(177,306)(178,307)(179,308)(180,309)(181,310)(182,311)(183,312)(184,313)
(185,314)(186,315)(187,316)(188,317)(189,318)(190,319)(191,320)(192,321)
(193,322)(194,323)(195,324)(196,325)(197,326)(198,327)(199,328)(200,329)
(201,330)(202,331)(203,332)(204,333)(205,334)(206,335)(207,336)(208,337)
(209,338)(210,339)(211,340)(212,341)(213,342)(214,343)(215,344);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(430)!( 2, 43)( 3, 42)( 4, 41)( 5, 40)( 6, 39)( 7, 38)( 8, 37)
( 9, 36)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 30)( 16, 29)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 45, 86)( 46, 85)
( 47, 84)( 48, 83)( 49, 82)( 50, 81)( 51, 80)( 52, 79)( 53, 78)( 54, 77)
( 55, 76)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)( 62, 69)
( 63, 68)( 64, 67)( 65, 66)( 88,129)( 89,128)( 90,127)( 91,126)( 92,125)
( 93,124)( 94,123)( 95,122)( 96,121)( 97,120)( 98,119)( 99,118)(100,117)
(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109)
(131,172)(132,171)(133,170)(134,169)(135,168)(136,167)(137,166)(138,165)
(139,164)(140,163)(141,162)(142,161)(143,160)(144,159)(145,158)(146,157)
(147,156)(148,155)(149,154)(150,153)(151,152)(174,215)(175,214)(176,213)
(177,212)(178,211)(179,210)(180,209)(181,208)(182,207)(183,206)(184,205)
(185,204)(186,203)(187,202)(188,201)(189,200)(190,199)(191,198)(192,197)
(193,196)(194,195)(217,258)(218,257)(219,256)(220,255)(221,254)(222,253)
(223,252)(224,251)(225,250)(226,249)(227,248)(228,247)(229,246)(230,245)
(231,244)(232,243)(233,242)(234,241)(235,240)(236,239)(237,238)(260,301)
(261,300)(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)
(269,292)(270,291)(271,290)(272,289)(273,288)(274,287)(275,286)(276,285)
(277,284)(278,283)(279,282)(280,281)(303,344)(304,343)(305,342)(306,341)
(307,340)(308,339)(309,338)(310,337)(311,336)(312,335)(313,334)(314,333)
(315,332)(316,331)(317,330)(318,329)(319,328)(320,327)(321,326)(322,325)
(323,324)(346,387)(347,386)(348,385)(349,384)(350,383)(351,382)(352,381)
(353,380)(354,379)(355,378)(356,377)(357,376)(358,375)(359,374)(360,373)
(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)(389,430)(390,429)
(391,428)(392,427)(393,426)(394,425)(395,424)(396,423)(397,422)(398,421)
(399,420)(400,419)(401,418)(402,417)(403,416)(404,415)(405,414)(406,413)
(407,412)(408,411)(409,410);
s1 := Sym(430)!( 1, 2)( 3, 43)( 4, 42)( 5, 41)( 6, 40)( 7, 39)( 8, 38)
( 9, 37)( 10, 36)( 11, 35)( 12, 34)( 13, 33)( 14, 32)( 15, 31)( 16, 30)
( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 44,174)( 45,173)
( 46,215)( 47,214)( 48,213)( 49,212)( 50,211)( 51,210)( 52,209)( 53,208)
( 54,207)( 55,206)( 56,205)( 57,204)( 58,203)( 59,202)( 60,201)( 61,200)
( 62,199)( 63,198)( 64,197)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)
( 70,191)( 71,190)( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)
( 78,183)( 79,182)( 80,181)( 81,180)( 82,179)( 83,178)( 84,177)( 85,176)
( 86,175)( 87,131)( 88,130)( 89,172)( 90,171)( 91,170)( 92,169)( 93,168)
( 94,167)( 95,166)( 96,165)( 97,164)( 98,163)( 99,162)(100,161)(101,160)
(102,159)(103,158)(104,157)(105,156)(106,155)(107,154)(108,153)(109,152)
(110,151)(111,150)(112,149)(113,148)(114,147)(115,146)(116,145)(117,144)
(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)
(126,135)(127,134)(128,133)(129,132)(216,217)(218,258)(219,257)(220,256)
(221,255)(222,254)(223,253)(224,252)(225,251)(226,250)(227,249)(228,248)
(229,247)(230,246)(231,245)(232,244)(233,243)(234,242)(235,241)(236,240)
(237,239)(259,389)(260,388)(261,430)(262,429)(263,428)(264,427)(265,426)
(266,425)(267,424)(268,423)(269,422)(270,421)(271,420)(272,419)(273,418)
(274,417)(275,416)(276,415)(277,414)(278,413)(279,412)(280,411)(281,410)
(282,409)(283,408)(284,407)(285,406)(286,405)(287,404)(288,403)(289,402)
(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)(296,395)(297,394)
(298,393)(299,392)(300,391)(301,390)(302,346)(303,345)(304,387)(305,386)
(306,385)(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)(313,378)
(314,377)(315,376)(316,375)(317,374)(318,373)(319,372)(320,371)(321,370)
(322,369)(323,368)(324,367)(325,366)(326,365)(327,364)(328,363)(329,362)
(330,361)(331,360)(332,359)(333,358)(334,357)(335,356)(336,355)(337,354)
(338,353)(339,352)(340,351)(341,350)(342,349)(343,348)(344,347);
s2 := Sym(430)!( 1,259)( 2,260)( 3,261)( 4,262)( 5,263)( 6,264)( 7,265)
( 8,266)( 9,267)( 10,268)( 11,269)( 12,270)( 13,271)( 14,272)( 15,273)
( 16,274)( 17,275)( 18,276)( 19,277)( 20,278)( 21,279)( 22,280)( 23,281)
( 24,282)( 25,283)( 26,284)( 27,285)( 28,286)( 29,287)( 30,288)( 31,289)
( 32,290)( 33,291)( 34,292)( 35,293)( 36,294)( 37,295)( 38,296)( 39,297)
( 40,298)( 41,299)( 42,300)( 43,301)( 44,216)( 45,217)( 46,218)( 47,219)
( 48,220)( 49,221)( 50,222)( 51,223)( 52,224)( 53,225)( 54,226)( 55,227)
( 56,228)( 57,229)( 58,230)( 59,231)( 60,232)( 61,233)( 62,234)( 63,235)
( 64,236)( 65,237)( 66,238)( 67,239)( 68,240)( 69,241)( 70,242)( 71,243)
( 72,244)( 73,245)( 74,246)( 75,247)( 76,248)( 77,249)( 78,250)( 79,251)
( 80,252)( 81,253)( 82,254)( 83,255)( 84,256)( 85,257)( 86,258)( 87,388)
( 88,389)( 89,390)( 90,391)( 91,392)( 92,393)( 93,394)( 94,395)( 95,396)
( 96,397)( 97,398)( 98,399)( 99,400)(100,401)(101,402)(102,403)(103,404)
(104,405)(105,406)(106,407)(107,408)(108,409)(109,410)(110,411)(111,412)
(112,413)(113,414)(114,415)(115,416)(116,417)(117,418)(118,419)(119,420)
(120,421)(121,422)(122,423)(123,424)(124,425)(125,426)(126,427)(127,428)
(128,429)(129,430)(130,345)(131,346)(132,347)(133,348)(134,349)(135,350)
(136,351)(137,352)(138,353)(139,354)(140,355)(141,356)(142,357)(143,358)
(144,359)(145,360)(146,361)(147,362)(148,363)(149,364)(150,365)(151,366)
(152,367)(153,368)(154,369)(155,370)(156,371)(157,372)(158,373)(159,374)
(160,375)(161,376)(162,377)(163,378)(164,379)(165,380)(166,381)(167,382)
(168,383)(169,384)(170,385)(171,386)(172,387)(173,302)(174,303)(175,304)
(176,305)(177,306)(178,307)(179,308)(180,309)(181,310)(182,311)(183,312)
(184,313)(185,314)(186,315)(187,316)(188,317)(189,318)(190,319)(191,320)
(192,321)(193,322)(194,323)(195,324)(196,325)(197,326)(198,327)(199,328)
(200,329)(201,330)(202,331)(203,332)(204,333)(205,334)(206,335)(207,336)
(208,337)(209,338)(210,339)(211,340)(212,341)(213,342)(214,343)(215,344);
poly := sub<Sym(430)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope